Has anyone considered that the siblings who come from further away may do so because their older brothers or sisters were admitted into the school in later years?
For example, local family decides to move out of London. This creates a vacancy in, say, Year 3. No-one local wants this space, their kids are all established in schools already. So the place goes to a child further away, perhaps a bus or car journey's distance. Perfectly legitimate. That child's younger sibling reaches reception age and therefore has some priority under current admissions.
Would it be right to change things so that sibling doesn't get a place? It would be okay to get a family to fill a vacancy higher up the school and travel for the privilege, but not for the next child to come too?
There's a good chance that the problem could be around infant school places rather than primary as a whole. That's something I would like to see the council do some research into.